The mayor gets elected every four years. Treasurer gets elected every six years. Both were elected this year. How many years before the election happens in the same year.

Step-by-step explanation:

The mayor gets selected once in every 4 years.

So, the number of years the mayor elections takes place

=  1, 4 ,8, 12, 16, 20, 24, 28,

Now, the Treasurer gets selected once in every 6 years.

So, the number of years the Treasurer elections takes place

= 1,  6, 12, 18, 24, 30

Now,as we can see from both statements, the year in which both elections happen are the common factors of 4 and 6.

The first common factor of 4 and 6 is 12.

So,in twelfth year both elections happen in the same year again.

Hence, there are 11 years before the elections happen in the same year.

i believe the answer is the polygon, heptagon.